\documentclass[a4paper,11pt]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[french]{babel}
\usepackage[a4paper,top=3.2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\usepackage{fancyhdr}
\usepackage{qrcode}
\usepackage[table]{xcolor}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
% Puces nettes (babel-french remplace sinon la puce par un tiret « – » peu pro).
% Vaut pour TOUTES les fiches qui importent ce module. AtBeginDocument pour
% passer après la personnalisation des listes faite par babel-french.
\AtBeginDocument{%
  \setlist[itemize]{leftmargin=1.8em,itemsep=0.5ex,topsep=0.4ex,parsep=0pt}%
  \setlist[itemize,1]{label=\textcolor{red!75!black}{\small\textbullet}}%
  \setlist[itemize,2]{label=\textcolor{red!75!black}{\scriptsize\textbullet}}%
}
% Titres compacts (gain de place vertical, fiches plus denses) — vaut pour tous.
\usepackage{titlesec}
\titlespacing*{\section}{0pt}{1.4ex}{0.6ex}
\titlespacing*{\subsection}{0pt}{1.0ex}{0.3ex}
% multicol : listes denses (calcul mental) sur 2 colonnes — neutre tant qu'il
% n'est pas utilisé, dispo pour tous les générateurs.
\usepackage{multicol}
\setlength{\columnsep}{1.5em}
% needspace : empêche un titre d'exercice de rester orphelin en bas de page
% (réserve quelques lignes ; sinon le titre passe à la page suivante avec sa
% liste). Neutre tant qu'il n'est pas appelé — dispo pour tous les générateurs.
\usepackage{needspace}
\usepackage{tikz}
\usetikzlibrary{decorations.text}

\usepackage{tgheros}
\pagestyle{fancy}
\fancyhf{}
\setlength{\headheight}{75pt}
\setlength{\headsep}{10pt}

\newcommand{\logowouf}{%
\begin{tikzpicture}[baseline={(current bounding box.center)},scale=0.55,
                    line cap=round,line join=round]
    \path[use as bounding box] (-2.20,-1.45) rectangle (2.20,2.20);
    \path[
        postaction={decorate},
        decoration={
            text along path,
            text={|\fontfamily{qhv}\bfseries\fontsize{9}{9}\selectfont|site2wouf.fr},
            text align={center},
            raise=0.03ex
        }
    ] (-1.29,0.48) arc[start angle=160,end angle=20,radius=1.29];
    \begin{scope}[xshift=-0.06cm]
        \fill[black] (-0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] ( 0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] (-0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black] ( 0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black]
            (0,-0.10)
            .. controls (-0.36,-0.02) and (-0.63,-0.24) .. (-0.58,-0.58)
            .. controls (-0.52,-0.93) and (-0.16,-1.12) .. (0,-0.90)
            .. controls (0.16,-1.12) and (0.52,-0.93) .. (0.58,-0.58)
            .. controls (0.63,-0.24) and (0.36,-0.02) .. (0,-0.10)
            -- cycle;
    \end{scope}
\end{tikzpicture}%
}

\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 33}

\fancyhead[C]{%
\raisebox{4pt}{%
\begin{minipage}[c]{0.15\textwidth}
    \centering
    \logowouf
\end{minipage}
\begin{minipage}[c]{0.62\textwidth}
    \centering
    {\Large\bfseries \titre\par}
    {\small\color{gray} \soustitre}
\end{minipage}
\begin{minipage}[c]{0.21\textwidth}
    \centering
    \qrcode[height=1.5cm]{https://site2wouf.fr/exercices_conversions_cycle3.php?x=33}\\[2pt]
    {\small\ttfamily\bfseries\color{red} CONV0033}
\end{minipage}%
}
}

\begin{document}

\begin{center}
    \small Fractions décimales, multiplication/division par 10, 100, 1 000, conversions d'unités.
\end{center}
\vspace{0.5em}
\sloppy

\needspace{5\baselineskip}
\section*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{94}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,094  ~ \(\times\)  ~ 10
\item   0,068  ~ \(\times\)  ~ 1 000
\item   0,034  ~ \(\times\)  ~ 100
\item   4,64  ~ \(\times\)  ~ 1 000
\item   659  ~ \(\times\)  ~ 100
\item   4,32  ~ \(\times\)  ~ 1 000
\item   517  ~ \(\times\)  ~ 1 000
\item   0,631  ~ \(\times\)  ~ 100
\item   9,59  ~ \(\times\)  ~ 1 000
\item   79,2  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   10,18  ~ : ~ 100
\item   3 596  ~ : ~ 1 000
\item   6 095  ~ : ~ 1 000
\item   537,1  ~ : ~ 1 000
\item   45,69  ~ : ~ 10
\item   58,98  ~ : ~ 1 000
\item   6,559  ~ : ~ 10
\item   1 904  ~ : ~ 100
\item   9 270  ~ : ~ 10
\item   2 541  ~ : ~ 10
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   8,36  ~ \(\times\)  ~ ... ~ = ~ 83,6
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 6,7
\item   36,5  ~ \(\times\)  ~ ... ~ = ~ 365
\item   0,702  ~ \(\times\)  ~ ... ~ = ~ 70,2
\item   0,621  ~ \(\times\)  ~ ... ~ = ~ 62,1
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 6,1
\item   8,13  ~ \(\times\)  ~ ... ~ = ~ 813
\item   80  ~ \(\times\)  ~ ... ~ = ~ 8 000
\item   0,397  ~ \(\times\)  ~ ... ~ = ~ 39,7
\item   12,2  ~ \(\times\)  ~ ... ~ = ~ 122
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   8,985  ~ \(\times\)  ~ 0,001
\item   526,7  ~ \(\times\)  ~ 0,01
\item   8 020  ~ \(\times\)  ~ 0,001
\item   15,34  ~ \(\times\)  ~ 0,01
\item   4,684  ~ \(\times\)  ~ 0,001
\item   67,59  ~ \(\times\)  ~ 0,01
\item   7,996  ~ \(\times\)  ~ 0,1
\item   66,07  ~ \(\times\)  ~ 0,01
\item   2 847  ~ \(\times\)  ~ 0,1
\item   53,39  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   29,26  ~ \(\times\)  ~ ... ~ = ~  0,292 6
\item   72,11  ~ \(\times\)  ~ ... ~ = ~  0,072 11
\item   6 134  ~ \(\times\)  ~ ... ~ = ~  6,134
\item   31,1  ~ \(\times\)  ~ ... ~ = ~  0,311
\item   16,11  ~ \(\times\)  ~ ... ~ = ~  0,016 11
\item   1 381  ~ \(\times\)  ~ ... ~ = ~  138,1
\item   319,1  ~ \(\times\)  ~ ... ~ = ~  0,319 1
\item   1 272  ~ \(\times\)  ~ ... ~ = ~  1,272
\item   0,281  ~ \(\times\)  ~ ... ~ = ~  0,000 281
\item   6 186  ~ \(\times\)  ~ ... ~ = ~  618,6
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~dam
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   4 299,9 ~cm~ = ...~hm
\item   2 833,8 ~mm~ = ...~dm
\item   3 073,9 ~dL~ = ...~L
\item   211,62 ~mL~ = ...~hL
\item   5 539,3 ~mL~ = ...~L
\item   279,19 ~kg~ = ...~cg
\item   714,15 ~hg~ = ...~g
\item   827,53 ~dL~ = ...~kL
\item   151,93 ~dm~ = ...~dam
\item   4 778,6 ~mg~ = ...~kg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{460}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{94}{10}\) = \(\dfrac{940}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{790}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,094  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,94}
\item   0,068  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 68}
\item   0,034  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,4}
\item   4,64  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 640}
\item   659  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 65 900}
\item   4,32  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 320}
\item   517  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 517 000}
\item   0,631  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 63,1}
\item   9,59  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 590}
\item   79,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 792}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   10,18 ~ : ~ 100 ~ = ~{\color{red} 0,101 8}
\item   3 596 ~ : ~ 1 000 ~ = ~{\color{red} 3,596}
\item   6 095 ~ : ~ 1 000 ~ = ~{\color{red} 6,095}
\item   537,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,537 1}
\item   45,69 ~ : ~ 10 ~ = ~{\color{red} 4,569}
\item   58,98 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 98}
\item   6,559 ~ : ~ 10 ~ = ~{\color{red} 0,655 9}
\item   1 904 ~ : ~ 100 ~ = ~{\color{red} 19,04}
\item   9 270 ~ : ~ 10 ~ = ~{\color{red} 927}
\item   2 541 ~ : ~ 10 ~ = ~{\color{red} 254,1}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   8,36 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~83,6
\item   0,067 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,7
\item   36,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~365
\item   0,702 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~70,2
\item   0,621 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~62,1
\item   0,061 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,1
\item   8,13 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~813
\item   80 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 000
\item   0,397 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~39,7
\item   12,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~122
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   8,985 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 985
}\item   526,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,267
}\item   8 020 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,02
}\item   15,34 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,153 4
}\item   4,684 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 684
}\item   67,59 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,675 9
}\item   7,996 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,799 6
}\item   66,07 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,660 7
}\item   2 847 ~ \(\times\)  0,1 ~ = ~{\color{red} 284,7
}\item   53,39 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,053 39
}\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   29,26 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,292 6
\item   72,11 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,072 11
\item   6 134 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,134
\item   31,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,311
\item   16,11 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,016 11
\item   1 381 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 138,1
\item   319,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,319 1
\item   1 272 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,272
\item   0,281 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 281
\item   6 186 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 618,6
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   4 299,9 ~cm~ = {\color{red}  0,429 99 }~hm
\item   2 833,8 ~mm~ = {\color{red}  28,338 }~dm
\item   3 073,9 ~dL~ = {\color{red}  307,39 }~L
\item   211,62 ~mL~ = {\color{red}  0,002 116 2 }~hL
\item   5 539,3 ~mL~ = {\color{red}  5,539 3 }~L
\item   279,19 ~kg~ = {\color{red}  27 919 000 }~cg
\item   714,15 ~hg~ = {\color{red}  71 415 }~g
\item   827,53 ~dL~ = {\color{red}  0,082 753 }~kL
\item   151,93 ~dm~ = {\color{red}  1,519 3 }~dam
\item   4 778,6 ~mg~ = {\color{red}  0,004 778 6 }~kg
\end{itemize}
\end{multicols}
\end{document}
